Algebra.Com's Answer #703893 by ikleyn(52800)![\"\"](\"/images/stars/stars-13.gif\")  
You can put this solution on YOUR website!
.
\n" );
document.write( "The  first four terms of gp is 30 and that of the last four term is 960 if the first term of gp is 1 find common ratio.
\n" );
document.write( "~~~~~~~~~~~~~~~~~~~\r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "\r\n" );
document.write( "If the first term is 1, then from the first part of the condition we have\r\n" );
document.write( "\r\n" );
document.write( " = 30. (1)\r\n" );
document.write( "\r\n" );
document.write( "I don't know how to solve it analytically for r (if do not use the Cardano's formula, which is, obviously, not from this opera).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "See the plot\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Plot y =  \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "I created a table in Excel, which shows that r is between 2.67 and 2.68,\r\n" );
document.write( "but it is clear that the graphical method (or any approximate \"technology\" method) \r\n" );
document.write( "is not what is expected as the solution method for this problem.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The second condition does not give much:\r\n" );
document.write( "\r\n" );
document.write( "it gives the second equation\r\n" );
document.write( "\r\n" );
document.write( " = 960, (2)\r\n" );
document.write( "\r\n" );
document.write( "with some unknown \"n\", which combined with (1) gives  =  = 32.\r\n" );
document.write( "\r\n" );
document.write( "but the condition does not give any clue for the value of n.\r\n" );
document.write( "\r\n" );
document.write( "So, although the \"technology\" can provide some approximate solution, \r\n" );
document.write( "looking into the problem \"in large\", I don't think that the condition is correct.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Again:\r\n" );
document.write( "\r\n" );
document.write( "the problem (as it is presented in the post) is reduced to two equations in two unknowns r and n\r\n" );
document.write( "\r\n" );
document.write( " = 30, (1) and\r\n" );
document.write( " = 32, (2)\r\n" );
document.write( "\r\n" );
document.write( "and I don't want (and don't know how) to go further.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It doesn't look to be attractive.\r\n" );
document.write( " \r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "--------------------
\n" );
document.write( "I thought one step further, and I am 170% sure that the presented formulation is incorrect.\r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "Indeed, from the plot (and from my Excel table) I just have the correct estimation for r ~ 2.67 -:- 2.68.\r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "Next, from equation (2) I have = 32 for some n.\r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "Now,  = 19.25, while  = 51.59.\r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "Hence, such integer positive \"n\" satisfying (1) and (2), simply DOES NOT EXIST.\r
\n" );
document.write( "
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "In conclusion, let me say THIS:\r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "It is VERY DIRTY BUSINESS to post incorrect problems to the forum.\r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "It costed me about 2 hours of my time, which I spent for NOTHING.\r
\n" );
document.write( "
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( " \n" );
document.write( " |